Originally Posted by late
And neither one of us said why it's important.
It's important because it's a direct measurment of the work you're doing. Before watts we measured heart rate, which is an excellent training tool. But a given heart rate doesn't tell you how much power you're putting into the pedals. Measuring output directly is a terrific advance, if expensive.
I think it is only practical to measure power output or watts directly on a stationary bike. If you are out riding on the road, your only real practical and convenient measure of power output is an indirect one like heart rate.